Measuring genomic pre-selection in theory and in...

2007

Paul VanRaden and Jan Wright Animal Improvement Programs Lab, Beltsville, MD [email protected]

2013

Measuring genomic pre-selection in theory and in practice

mailto:[email protected]

Interbull annual meeting, Nantes, France, August 2013 (2) Paul VanRaden 2013

Traditional mixed models do not account for genomic selection • Phenotypes only for animals with

highest Mendelian sampling • GBV differ from EBV for progeny,

mates, parents, or herdmates

Multi-step methods may be biased Single-step methods reduce bias

In Theory


1-Step Relationship Inverse Aguilar et al. (2010)

H-1 = A11 A12 A21 A22 + G-1 - A22

-1

1 = non-genotyped animals (60 million) 2 = genotyped animals (400,000)


Animal model • EBV = w1 PA + w2 YD + w3 PC • (parent average, yield deviation,

progeny contribution)

1-step genomic info (GI) model • GBV = w1PAg + w2YDg + w3PCg + w4GI • GI = ∑off-diagonalj of G-1–A22

-1(GBVj) divided by diagonali of G-1–A22

-1 • Numerator of w4 in denominator of w

Traditional and 1-Step Models


Computed for 8,300 Brown Swiss Diagonals of G and A22 are similar

• G: mean FG = 3.98% and SD = 4.15% • A22: mean FA = 3.95% and SD = 2.97%

Diagonals of G-1 larger than A22-1

• Mean = 5.83 for G, 2.18 for A22 • G-1, A22

-1 and difference all highly correlated

Diagonals of G-1–A22-1


G A G-1 A-1 G-1 - A-1 G 1.0 .70 .05 .03 .06 A 1.0 .02 -.02 .04 G-1 1.0 .98 .99 A-1 1.0 .94 G-1 - A-1 1.0

Correlations of Diagonals Genotyped Brown Swiss


Phenotyped only animals with good Mendelian sampling genotypes

Discrete or overlapping generations • Bias if discrete (Patry, Ducrocq 2011) • OK with overlap (Nielsen et al, 2012) • Large bias for dams (Liu et al, 2009)

Actual studies of pre-selection and genomic assortative mating needed

Simulations of Pre-Selection Bias


Test actual selection and mating Quantify genomic pre-selection in:

• Mates of proven bulls (group 1) • Mates of young bulls (group 2) • Dams of young selected sons

Measure future bias because pre-selection has already occurred

In Practice


Percentage of Genotyped Mates Group 2 bulls ranked by NM$

0

10

20

30

40

50

60

70

80

90

100

700 725 750 775 800 825 850 875 900 925

Maurice

Elvis ISY Altatrust

Fernand

Net Merit (Aug 2013)

Perc

enta

ge o

f mat

es g

enot

yped

Supersire

Numero Uno

S S I Robust Topaz

Garrold

Mogul


Group 1 (proven bulls) • Daughters with records • Top 50, no dtrs in April 2010 • Were mates pre-selected?

Group 2 (young bulls) • Top 50, born 2009 and 2010 • Study calves born in USA • Will pre-selected mates cause bias?

Mates of Group 1 and 2 Bulls


Trait Mean SD Min Max NM$ 2 4 -5 13 Protein 0 0 -1 1 Prod Life .0 .0 .0 .1 Dtr Preg Rate .0 .0 .0 .1 SCS .00 .00 -.01 .01 Final Score .00 .01 -.04 .02 Udder Depth .00 .01 -.02 .02

Group 1 Realized Mate Bias


Trait Mean SD Min Max NM$ 8 9 0 33 Protein 0 0 0 1 Prod Life .1 .1 .0 .5 Dtr Preg Rate .1 .1 .0 .3 SCS -.01 .01 -.03 .00 Final Score .02 .03 -.01 .10 Udder Depth .03 .04 -.01 .13

Group 2 Future Bias from Mates


Dams with ≥ 1 sampled son born 2008 to 2012

Son selection differential = ∑(GPTA – PA) / # of sons sampled

Dam’s bias = 2 * sons’ selection differential * (DE from sampled sons) / (total conventional DE) • DE = daughter equivalents or EDC

Future Bias – Dams of Young Bulls


29 sons genotyped, 6 selected, each will provide 5.4 DE

Son selection differential for milk = ∑(GPTA – PA) / 6 = 583 pounds

30 daughters, each provide 1.5 DE 8.3 DE from PA, 7.8 from records Dam’s future bias = 2 * 583 * 6 * 5.4

/ [8.3 + 7.8 + 6 * 5.4 + 30 * 1.5] = 808

Example Dam HOUSA000065597532


Trait Mean SD Min Max NM$ 29 33 -124 156 Protein 1 3 -10 14 PL .3 .5 -1.7 2.0 DPR .1 .2 -.9 .9 SCS -.01 .04 -.22 .14

Expected Future Bias – Bull Dams


Also from preferential treatment • High-priced early daughters • Lack of random sampling

Deregression removes some bias • Example: dam gets credit only for

own records and non-genotyped progeny, not genotyped sons

• Use matrix instead of simple one at a time deregression

Potential Biases


Conclusions

Evaluations should adjust for GBV instead of EBV of: • Progeny, mates, contemporaries, and

parents Biases from pre-selection:

• Very small for recently proven bulls • Moderate from mates top young bulls • Will be large for dams of several highly

selected sons, but deregression can remove some of the bias


Phenotypes, genotypes, and pedigrees were provided by the Council on Dairy Cattle Breeding

Acknowledgments

Measuring genomic pre-selection in theory and in...

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